SOUTHWEST RESEARCH INSTITUTE ®

6220 CULEBRA ROAD  POST OFFICE DRAWER 28510  SAN ANTONIO, TEXAS, USA 78228-0510  (210) 684-5111  www.swri.org 

ENGINE, EMISSIONS, AND VEHICLE RESEARCH DIVISION HTTP://ENGINEANDVEHICLE .SWRI.ORG

FAX: (210) 522-3950 ISO 9001 Certified 

ISO 14001 Certified 

SAN ANTONIO, TEXAS 

HOUSTON, TEXAS  WASHINGTON, DC  ANN ARBOR, MI 

 February 8, 2011 

Mr. Joseph Bachman 

USEPA Headquarters 

Ariel Rios Building 

1200 Pennsylvania Avenue, N. W. 

Mail Code: 6406J 

Washington, DC 20460

SUBJECT: SwRI® Final Report 03-15194.02 Titled, "Heavy-Duty Wheel and Tire 

Combination Rotational Inertia Study” 

1.0 INTRODUCTION

 Chassis dynamometers attempt to reproduce the forces acting on vehicles as they are 

operated on the road. The two major loads imparted on vehicles are typically referred to as road 

load and inertia. Road load is force created by the force associated with aerodynamic drag, tire 

deflection, and driveline components. Inertia is the resistance to changes in acceleration and is 

the primary load on vehicles during transient operation. 

 Chassis dynamometer testing of heavy-duty vehicles has historically been conducted to 

compare two different components or technologies on the same vehicle chassis. However, new 

regulations have been proposed to measure the absolute value of fuel economy and emissions. 

This means that more accurate values of road load and inertia are required to meet the 

expectations of chassis dynamometer results. 

Vehicles are typically mounted on a chassis dynamometer by locating the driven tires on 

the dynamometer rolls and using chocks and straps on the non-driven tires to keep the vehicle 

positioned during testing, as shown in Figure 1. Since the steer tires are not rotating during 

testing, the linear mass of their rotational inertia must be added to the test weight of the vehicle 

for accurate results. Rotational inertia of stationary wheel/tire combinations has typically been 

assumed to be between three and five percent of the equivalent linear inertia of a typical vehicle. 

However, this estimation does not accurately reflect the effect of a chosen wheel and tire 

combination on fuel economy or the number of stationary wheels. For example, taller, heavier 

wheels and tires have more inertia than lighter, shorter combinations. Therefore, the benefits of 

lower inertia combinations would not be reflected in chassis dynamometer testing if their inertia 

estimation was based on a percentage of vehicle test weight. In addition, the estimation does not 

consider the number of stationary wheels. Figure 2 is a diagram of a Class 8 tractor-trailer 

equipped with eighteen wheels, resulting in ten stationary wheels compared to two stationary 

wheels for vehicles without a trailer. This study is intended to both provide a more accurate 

calculation of rotational inertia and provide the ability to more accurately reflect the fuel 

economy benefit of reducing rotational inertia. 
Mr. Joseph Bachman 

Environmental Protection Agency 

February 8, 2011 

Page 2 of 9 

Report 03.15194.02 

FIGURE 1. DIAGRAM OF HEAVY-DUTY VEHICLE INSTALLED 

ON A CHASSIS DYNAMOMETER 

FIGURE 2. DIAGRAM OF CLASS 8 TRACTOR-TRAILER INSTALLED 

ON A CHASSIS DYNAMOMETER 

 

S

D

D

D

D

S

S

Drive Simulated

D D

R R

D

D

D

D

Dynamometer

Rolls

S

S

S

S

D

D

D

D

D

D

D

D

S

S

Simulated Simulated Drive

S S D D S

Dynamometer R R

Rolls

S

S

S

S

Note: Trailer not present during

dynamometer testing
Mr. Joseph Bachman 

Environmental Protection Agency 

February 8, 2011 

Page 3 of 9 

Report 03.15194.02 

2.0 TESTING

Five of the most common wheel and tire combinations were purchased from a local 

supplier for the purpose of measuring each combination’s inertia. A description of each 

combination is listed in Table 1. 

TABLE 1. DESCRIPTION OF EACH COMBINATION 

CONSIDERED FOR THIS PROJECT 

 

Combination Number 

1 2 3 4 5 

Wheel Material Aluminum Steel Aluminum Steel Aluminum 

Wheel Size, 

Diameter X 

Width (in) 24.5 X 8.25 24.5 X 8.25 22.5 X 8.25 22.5 X 8.25 22.5 X 14 

Tire Size R675/11R24.5 R67511R24.5 295/75R22.5 295/75R22.5 445/50R22.5 

2.1 Test Stand Description 

The test stand that was used for this testing is one of SwRI’s Virtual Vehicle 

Transmission Test Cells (VVTTC). The continuous power rating of this motor is 310 kW from 

6000 rpm to a maximum speed of 9000 rpm. The motor can produce a maximum continuous 

torque of 493 N-m from zero to 6000 rpm. For the purposes of this testing the dynamometer was 

operated in torque control mode. Operating the dynamometer in this mode allows the user to 

deliver a constant torque up to a specified speed limit. The VVTTC provides excellent control 

accuracy when operating in this manner. Custom fixtures were designed and fabricated to allow 

the wheel/tire combination to be mounted to a headstand. The headstand was driven by a 

driveshaft connected to an HBM T10FS torque meter mounted directly to the input 

dynamometer. Figure 3 shows Combination 5 installed on the test stand. 
Mr. Joseph Bachman 

Environmental Protection Agency 

February 8, 2011 

Page 4 of 9 

Report 03.15194.02 

FIGURE 3. TEST STAND SETUP 

2.1 Measured Combination Inertia 

 The inertia of the drive assembly was measured by accelerating it at various rates without 

a combination mounted. Each combination was then mounted on the drive assembly and 

accelerated to a desired speed limit using a constant command torque. This test method 

produces data showing constant torque and constant acceleration over a significant period of 

time allowing inertia to be calculated as torque divided by acceleration. Figure 4 shows an 

example of the data generated during one of the tests. Table 2 is a summary of each 

Combination’s mass and measured inertia. 

FIGURE 4. SPEED AND TORQUE PROFILE 

Ramped Speed @ Constant Torque for Tire/Wheel

0

20

40

60

80

100

120

140

160

180

200

0 5 10 15 20 25 Time (s)

Tire Speed

(RPM)

Torque (N-m)
Mr. Joseph Bachman 

Environmental Protection Agency 

February 8, 2011 

Page 5 of 9 

Report 03.15194.02 

TABLE 2. MASS AND MEASURED INERTIA OF EACH COMBINATION 

Combination Number 

1 2 3 4 5 

Mass (kg) 77.1 88.5 77.1 63.5 107 

Inertia (kg-m2) 13.2 14.8 12.4 9.97 18.9 

2.3 Calculated Combination Inertia 

The wheel inertia was treated as two separate pieces, with the outer rim treated as a thinwalled cylinder and the inner wheel portion treated as a hollow cylinder, as shown in Figure 5. 

The weight of each portion of the wheel was assumed to correspond to its surface area, the 

weight was assumed to be spread evenly upon the surface, and all design details were ignored. 

The inertia can be calculated from the mass and radii of each element using Equations 1 and 2. 

The calculated inertia values for each wheel are shown in Table 3. 

FIGURE 5. DIAGRAM OF WHEEL ELEMENTS USED 

TO CALCULATE WHEEL INERTIA 

 
Mr. Joseph Bachman 

Environmental Protection Agency 

February 8, 2011 

Page 6 of 9 

Report 03.15194.02 

TABLE 3. WHEEL PARAMETERS USED TO ESTIMATE THEROTATIONAL 

INERTIA OF EACH COMBINATION 

Wheel 

Parameters 

Combination Number 

1 2 3 4 5 

Mass (kg) 27.3 40.8 34.5 20.7 32.4 

Width (m) 0.254 0.254 0.254 0.254 0.381 

Outer Diameter 

(m) 

0.610 0.610 0.572 0.572 0.572 

Inner Diameter 

(m) 

0.222 0.222 0.222 0.222 0.222 

Equation 1. Inertia of a Thin-Walled Cylinder 

I= m r2

 

m= mass of hollow cylinder 

r = distance between axis and cylinder mean radius 

Equation 2. Inertia of a Hollow Cylinder 

I=(1/2) m (ri + ro )

2 

m= mass of hollow cylinder 

ri = distance between axis and inside hollow cylinder 

ro= distance between axis and outside hollow cylinder

The tire inertia was calculated as hollow cylinder using three elements, the tread and each 

sidewall, as shown in Figure 4. The density and thickness of the tire was assumed to be uniform 

throughout each element. Table 4 lists the values used for calculating the inertia of each tire. 

The sidewalls were assumed to be identical; therefore, the mass listed in Table 4 is the mass of 

both sidewalls. 
Mr. Joseph Bachman 

Environmental Protection Agency 

February 8, 2011 

Page 7 of 9 

Report 03.15194.02 

FIGURE 4. DIAGRAM OF TIRE ELEMENTS USED 

TO CALCULATE WHEEL INERTIA 

TABLE 4. TIRE PARAMETERS USED TO ESTIMATE THE 

ROTATIONAL INERTIA OF EACH COMBINATION

Tire Parameters 

Combination Number 

1 2 3 4 5 

Tread

Mass (kg) 22.7 22.7 20.4 20.4 49.4 

Outer radius (m) 0.550 0.550 0.506 0.506 0.506 

Inner radius (m) 0.526 0.526 0.482 0.482 0.474 

Both Sidewalls 

Total mass (kg) 23.7 23.7 20.4 20.4 23.8 

Outer radius (m) 0.508 0.508 0.464 0.464 0.457 

Inner radius (m) 0.305 0.305 0.279 0.279 0.273 
Mr. Joseph Bachman 

Environmental Protection Agency 

February 8, 2011 

Page 8 of 9 

Report 03.15194.02 

 Table 5 lists the calculated inertia for each wheel and tire and the total calculated inertia 

for each combination. The total measured inertia values are shown to compare to the empirical 

values. The difference between the empirical and calculated values was between 13 and 10 

percent for Combinations 1 and 2, the 24.5 inch wheel sets. The difference was much less for 

Combinations 3 through 5, 22.5 wheel sets, including the “Super Single.” The difference ranged 

between 5.9 and 1.3 percent. 

TABLE 5. ESTIMATED ROTATIONAL INERTIA VALUES 

COMPARED TO EMPIRICAL VALUES 

Combination Number 

1 2 3 4 5 

Calculated Tire Inertia, kg-m2 10.1 10.1 7.49 7.49 14.1 

Calculated Wheel Inertia, kg-m2 4.62 6.82 5.17 3.10 5.04 

Total Calculated Inertia, kg-m2 14.8 17.0 12.7 10.6 19.1 

Total Measured Inertia, kg-m2 13.2 14.8 12.4 10.0 18.9 

Percent Difference 10% 13% 2.2% 5.9% 1.3% 

4.0 SUMMARY 

 Five different wheel and tire combinations acquired for the purpose of determining the 

linear equivalent mass of each combination in order to accurately simulate the non-drive tires’ 

inertia during chassis dynamometer testing. Each combination was mounted on an electric 

dynamometer and accelerated by a constant torque, resulting in constant acceleration value used 

to directly calculate inertia. 

 The purpose of the study was to determine whether or not the estimate of three percent of 

vehicle test weight was appropriate. Vehicle test weights are dependent on the vehicle’s 

purpose. For instance, the test weight for a bus is the bus’s empty weight plus half the passenger 

load plus driver multiplied by 68 kg. However, a utility truck is typically always loaded to its 

Gross Vehicle Weight Rating (GVWR) due the boom and associated equipment mounted on the 

truck. Class 8 tractor-trailers are typically loaded to seventy percent of their fully loaded 

weight. 

Table 6 lists the GVW for Classes 5 through 8, for which the wheel and tire combinations 

tested are normally used, along with the test weight of seventy percent of GVW for each class. 

The number of wheels that must have inertia simulated is shown in the third line of Table 6. 

Most Class 5 through Class 7 vehicles do not normally pull trailers, so only the front tires must 

be simulated, but Class 8 tractor-trailers typically have eight trailer tires in addition to the two 

front tires. The table shows the additional inertia added using the estimation of three percent of 

test weight and the empirical values after being converted to linear mass. The linear mass 

equivalent of each combination is calculated by dividing the rotational inertia value by the 

effective radius, which is the outer radius of the tire, in this case. 
Mr. Joseph Bachman 

Environmental Protection Agency 

February 8, 2011 

Page 9 of 9 

Report 03.15194.02 

TABLE 6. COMPARISON OF STANDARD THREE PERCENT ASSUMPTION 

VALUES AND MEASURED INERTIA VALUES USED FOR ESTIMATING 

 INERTIA OF STATIONARY WHEELS DURING 

CHASSIS DYNAMOMETER TESTING 

   Class 5 Class 6 Class 7 Class 8

Gross Vehicle Weight (GVW), kg 8840 11800 15000 36000

Test Weight (70 percent of GVW), kg 6190 8250 10500 25400

Number of stationary wheels 2 2 2 10

3% of test weight, kg 186 248 314 762

Empirical values , kg 49.0 49.0 49.0 245

Net difference , kg 137 199 265 517

Percent difference vs. test weight 2.2% 2.4% 2.5% 2.0%

The net differences, in this example, for Classes 5 through 8 are 137 kg, 199 kg, 265 kg, 

and 517 kg, respectively. The percent difference between the standard assumption and the 

measured values compared to test weight vary between 2.0 and 2.5 percent. The difference 

between the previous three percent of test weight assumption and the measured values show that 

for A-B comparisons of a technology on the same vehicle is close enough to the actual inertia 

values for valid experiments, however, for absolute fuel economy and emission tests, the 

measured values will likely produce more accurate results. 

Prepared by: Reviewed by: 

 

Joseph W. Anthony Vlad Ulmet 

Senior Research Engineer Manager 

Emissions Research and Development Emissions Research and Development 

 Department Department 

/mab